Cosmic inflation provides a natural framework for the production of primordial blackholes.
Single field inflation is capable of generating large primordial curvature perturbation in small scales compared to the scale of the cosmic microwave background [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}.
Once the mode with large curvature perturbation reenters the horizon, gravitational collapse may occur, thereby forming primordial blackholes.
Single field models with a canonical kinetic term and minimal coupling to the gravity, however, require a severe fine-tuning of the scalar potential to generate an inflection point near the end of inflation that produces large enough density perturbations [14]}.
It has also been pointed out that the standard slow-roll approximation breaks down near the inflection point [14]}, [16]}.
In multifield inflation, e.g. in hybrid inflation models, generation of primordial blackholes is less challenging; see Refs. [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}.
Other models for generating large primordial curvature perturbation during inflation include the one with the modified gravity sector, and with a non-canonical form of the inflaton; see e.g. Refs. [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}.
It is also possible to produce primordial blackholes during (p)reheating [36]}, [37]}, [38]}, [39]}.
